What does it mean, exactly, for a given system to be a 'neural correlate of consciousness'?

Almost everyone agrees that there will be very strong correlations between what's in the brain and consciousness,

Here, the broader issues are already familiar, and discussion has focused at a more sophisticated and detailed level. Within the philosophy of mind, the problem of consciousness is no big news.

Anyway, there is a lot of really interesting work going on in the neuroscience and psychology of consciousness, and I would love to see philosophers become more closely involved with this.

Even when I was studying mathematics, physics, and computer science, it always seemed that the problem of consciousness was about the most interesting problem out there for science to come to grips with.

Studying consciousness tells us more about how the world is fundamentally strange. I think we have a few revolutions to go yet before we get to the bottom of it.